Problem: Solve for $x$ and $y$ using elimination. ${4x-2y = 12}$ ${5x+2y = 33}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $9x = 45$ $\dfrac{9x}{{9}} = \dfrac{45}{{9}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {4x-2y = 12}\thinspace$ to find $y$ ${4}{(5)}{ - 2y = 12}$ $20-2y = 12$ $20{-20} - 2y = 12{-20}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {5x+2y = 33}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ + 2y = 33}$ ${y = 4}$